X तथा Y ज्ञात कीजिए यदि X + Y = $ \left[\begin{array}{ll}7 & 0 \\ 2 & 5\end{array}\right]$ तथा X - Y = $\left[\begin{array}{ll}3 & 0 \\ 0 & 3\end{array}\right]$
Exercise-3.2-7(1)
Download our app for free and get started
दिया है,
X + Y = $ \left[\begin{array}{ll} 7 & 0 \\ 2 & 5 \end{array}\right] $ ...(i)
तथा X - Y = $ \left[\begin{array}{ll} 3 & 0 \\ 0 & 3 \end{array}\right] $ ...(ii)
समी (i) तथा (ii) को जोड़ने पर,
2X = $\left[\begin{array}{ll} 7 & 0 \\ 2 & 5 \end{array}\right]$ + $ \left[\begin{array}{ll} 3 & 0 \\ 0 & 3 \end{array}\right]$ = $\left[\begin{array}{rr} 10 & 0 \\ 2 & 8 \end{array}\right]$ $\Rightarrow$ X = $\frac{1}{2}$$\left[\begin{array}{rr} 10 & 0 \\ 2 & 8 \end{array}\right]$= $\left[\begin{array}{ll} 5 & 0 \\ 1 & 4 \end{array}\right] $
समी (i) में से समी (ii) को घटाने पर,
2Y = $\left[\begin{array}{ll} 7 & 0 \\ 2 & 5 \end{array}\right]$ - $\left[\begin{array}{ll} 3 & 0 \\ 0 & 3 \end{array}\right]$ = $\left[\begin{array}{ll} 4 & 0 \\ 2 & 2 \end{array}\right]$ $\Rightarrow$ Y = $\frac{1}{2}$$ \left[\begin{array}{ll} 4 & 0 \\ 2 & 2 \end{array}\right]$ = $ \left[\begin{array}{ll} 2 & 0 \\ 1 & 1 \end{array}\right] $
X + Y = $ \left[\begin{array}{ll} 7 & 0 \\ 2 & 5 \end{array}\right] $ ...(i)
तथा X - Y = $ \left[\begin{array}{ll} 3 & 0 \\ 0 & 3 \end{array}\right] $ ...(ii)
समी (i) तथा (ii) को जोड़ने पर,
2X = $\left[\begin{array}{ll} 7 & 0 \\ 2 & 5 \end{array}\right]$ + $ \left[\begin{array}{ll} 3 & 0 \\ 0 & 3 \end{array}\right]$ = $\left[\begin{array}{rr} 10 & 0 \\ 2 & 8 \end{array}\right]$ $\Rightarrow$ X = $\frac{1}{2}$$\left[\begin{array}{rr} 10 & 0 \\ 2 & 8 \end{array}\right]$= $\left[\begin{array}{ll} 5 & 0 \\ 1 & 4 \end{array}\right] $
समी (i) में से समी (ii) को घटाने पर,
2Y = $\left[\begin{array}{ll} 7 & 0 \\ 2 & 5 \end{array}\right]$ - $\left[\begin{array}{ll} 3 & 0 \\ 0 & 3 \end{array}\right]$ = $\left[\begin{array}{ll} 4 & 0 \\ 2 & 2 \end{array}\right]$ $\Rightarrow$ Y = $\frac{1}{2}$$ \left[\begin{array}{ll} 4 & 0 \\ 2 & 2 \end{array}\right]$ = $ \left[\begin{array}{ll} 2 & 0 \\ 1 & 1 \end{array}\right] $
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1परिकलित कीजिए: $\left[\begin{array}{rrr} -1 & 4 & -6 \\ 8 & 5 & 16 \\ 2 & 8 & 5 \end{array}\right]$ + $\left[\begin{array}{ccc} 12 & 7 & 6 \\ 8 & 0 & 5 \\ 3 & 2 & 4 \end{array}\right]$View Solution
- 2यदि A = $\left[\begin{array}{lll}3 & \sqrt{3} & 2 \\ 4 & 2 & 0\end{array}\right]$ तथा B = $\left[\begin{array}{rrr}2 & -1 & 2 \\ 1 & 2 & 4\end{array}\right]$ तो $\left(\mathrm{A}^{\prime}\right)^{\prime}$ = A को सत्यापित कीजिए।View Solution
- 3यदि $A = \left[\begin{array}{lll} 1 & 0 & 2 \\ 0 & 2 & 1 \\ 2 & 0 & 3 \end{array}\right]$ है तो सिद्ध कीजिए कि $A^{3 }- 6A^{2 }+ 7A + 2I = 0$View Solution
- 4यदि A = $ \left[\begin{array}{ccc}1 & 1 & -1 \\ 2 & 0 & 3 \\ 3 & -1 & 2\end{array}\right]$, B = $\left[\begin{array}{cc}1 & 3 \\ 0 & 2 \\ -1 & 4\end{array}\right]$ तथा C = $\left[\begin{array}{cccc}1 & 2 & 3 & -4 \\ 2 & 0 & -2 & 1\end{array}\right]$ तो A(BC) तथा (AB)C ज्ञात कीजिए और दिखलाइए कि (AB)C = A(BC) है।View Solution
- 5View Solutionयदि किसी आव्यूह में 24 अवयव हैं तो इसकी संभव कोटियाँ क्या हैं? यदि इसमें 13 अवयव हों तो कोटियाँ क्या होंगी?
- 6दर्शाइए कि $\left[\begin{array}{rr}5 & -1 \\ 6 & 7\end{array}\right]\left[\begin{array}{ll}2 & 1 \\ 3 & 4\end{array}\right] $ $\neq$ $\left[\begin{array}{ll}2 & 1 \\ 3 & 4\end{array}\right]\left[\begin{array}{rr}5 & -1 \\ 6 & 7\end{array}\right]$View Solution
- 7निदर्शित गुणनफल परिकलित कीजिए:$\left[\begin{array}{rr} 1 & -2 \\ 2 & 3 \end{array}\right]$$\left[\begin{array}{lll} 1 & 2 & 3 \\ 2 & 3 & 1 \end{array}\right]$View Solution
- 8यदि A = $ \left[\begin{array}{rr} 0 & -1 \\ 0 & 2 \end{array}\right]$ तथा B = $\left[\begin{array}{ll} 3 & 5 \\ 0 & 0 \end{array}\right] $ है तो AB का मान ज्ञात कीजिए।View Solution
- 9आव्यूहों का परिवर्त ज्ञात कीजिए: $\left[\begin{array}{rr} 1 & -1 \\ 2 & 3 \end{array}\right]$View Solution
- 10यदि A = $ \left[\begin{array}{r} -2 \\ 4 \\ 5 \end{array}\right]$, B = $\left[\begin{array}{lll} 1 & 3 & -6 \end{array}\right] $ है तो सत्यापित कीजिए (AB)$^{\prime}$ = B$^{\prime}$A$^{\prime} $ है।View Solution